CLASS-7
INTRODUCTION OF INTEGERS

INTEGERS

As we know that, the collection of numbers …………, -7, -6, - 5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7,..………. are called integers whereas …………, -7, -6, - 5, -4, -3, -2,…… are called negative integers and 1, 2, 3, 4, 5, 6, 7,..………. are called positive integers. The integers zero ‘0’ is neither positive nor negative integers. The set of integers is denoted by I or Z and N ⊆ I or Z and W ⊆ I or Z.

The numbers .…………,-3,-2,-1,0,1,2,3,……… are called Integers. The natural numbers 1,2,3,4,……… are called Positive Integers.

The numbers -1,-2,-3,-4,…… are called Negative Integers. The number 0 is an integer. It is neither positive nor negative.

Thus,integers form a bigger collection of numbers which contain whole numbers and the negative numbers -1,-2,-3,……

To be remembered –

a) All positive integers are more than Zero and all negative integers are less than zero.

b) All and every positive integers are greater than all and every negative integers

c) Given two positive integers, the one with the bigger absolute value is greater, and given two negative integers, the one with the smaller absolute value is greater.

d) The absolute value of an integer is the whole number obtained by disregarding its sign, the absolute value of an integers ‘b’ is denoted by  (+b)    

The line drawn above is called the Number line. From the number line, we observe that:

Ø There is no largest integer and there is no smallest integer.

Ø An integer is greater than all those integers that lie to its left on the number line.

Ø An integer is less than all those integers that lie to its right on the number line.

Ø There is no integer between any two consecutive integers and there is at least one integer between two non-consecutive integers.

Consecutive integers means the integers next to one-another.

For example:-

* * There is no integer between two consecutive integers 5 and 6.

* * There is no integer between two consecutive integers -6 and -5.

* * The integer -5 lies between two non-consecutive integers -6 and

-4. Obviously, -6 < -5 and -5 < -4, we may write -6 < -5 < -4.

** The integers -3 and 4 lie between two non-consecutive integers -5 and 6. Obviously, -5 < -3 < 6 and -5 < 4 < 6.